Our approach is more general in that we do not assume the strong subsystem structure imposed by conditions 2) and 3).
As such, our work strengthens Coecke's argument that non-signalling can be derived from a simpler condition [1]} (Appendix ).
In general, our top-down view can be taken as a precursor and sanity check for process theories.
In complex global theories, a strong subsystem structure may not be clear cut from the start. The cautious researcher can first use our approach to test different reduced descriptions for independence conditions. If she succeeds in finding independent effective spaces — which is not always possible — she may then frame them as subsystems and attempt a modular construction.
